In the gastronomic sense, at least, David Cameron's message to Europe's leaders seems to be working. The usual routine is that EU chiefs meet in Brussels for a summit and kick off in the evening with a three-course dinner. On Thursday evening the leaders sat down to an austere supper of cold cuts as they prepared for the ritual psycho-drama that comes up every seven years, the mindnumbing number-crunching over who gets what from the trillion-euro EU budget that is to fund the union from 2014 until 2020.

It's a grinding, gruelling way of doing business, seemingly destined for dysfunction. Anywhere else on the European conference circuit, people meet in the morning, do their business through the day and top things off with dinner. But the leaders kicked off at 8pm, bracing themselves for an extremely long night of bleary-eyed arithmetic. Martial metaphors are to the fore. Red lines, battles, shoring up the defences, duels, and showdowns. And they're supposed to be friends.

The evidence mounts by the week that there has to be a better way of doing these things. The most recent summit, a month ago, kicked off as usual in the evening, went on until 5am, resumed again four hours later, and wound up with a demoralising failure, unable to agree anything.

Since then the finance ministers of the single currency zone have met three times to grapple with Greece, again all evening sessions running until 4 or 5 in the morning. Stalemate and failure, three in a row.

As a result, these get-togethers are enveloped by an air of weariness foretold. The prospects of a gamechanger look remote. Indeed, the Austrian chancellor, Werner Faymann, has already groaned about a wasted weekend by suggesting the two-day summit would go on until Sunday and still result in no deal.

To reduce these budget battles to their essentials, the pattern over the decades, or at least since Margaret Thatcher's epic victory in 1984, has been for the French to get everyone else to pay for their farmers, Britain to whinge and be compensated for that by a budget "rebate", and Germany to surrender its credit cards to make it all possible. That pattern persists but has shifted over the past decade because of the unification of Europe, with 10 east European poor countries joining and requiring vast transfers of "cohesion" funds to try to level the EU.

Poland, for example, is almost certain to be the biggest winner of the current bunfight whatever the outcome, standing to gain around €10bn a year in development funds until 2020. It has not escaped the attention of diplomats and officials that Janusz Lewandowski, the commissioner in charge of the budget, happens to be Polish.

The fundamental fight is between those who pay and those who get. Those who pay – nine countries, or a third of the EU – want a smaller overall budget. The other two thirds do not.

But within these two clubs, the divisions are acute. The givers include Britain, Germany, France and Italy. The British and the French will never agree on what the budget is for. And among the takers, the Hungarians are losing big time, while the Poles are coining it. So no love lost there, either.

The day started on Thursday morning with Cameron, identified by most as the biggest troublemaker, being interviewed by the EU's chief fixer, Herman Van Rompuy, for 35 minutes to try to establish the UK's bottom line. Each side had two "goons" in the room, in Downing Street parlance. These pre-summit one-on-one "confessionals" ran all-day until the 8.30pm supper. If they started with the biggest problem, Cameron, they finished with the person who will have to supply the solution if one is to be found – the most experienced politician at the summit, Chancellor Angela Merkel. Cameron's early start left him with plenty of time to fill, so he had a 90-minute lunch at the brasserie next to the British embassy.

The differences are huge – about €200bn – between what the commission originally proposed, €1,091bn euros, and what the British refuse to say is their figure, around €890bn.

In the meantime, Van Rompuy has crafted a compromise of €940bn for the seven years of the next budget. The British said this can still be slashed by "tens of billions".

In recent days the emphasis of Cameron's remarks has been on defending the sanctity of the British rebate, worth between €3bn and €4bn a year. But the rebate is not really in danger. This looks like a diversion, pretending to fight a battle that has already been won. The real issue is the overall level of spending, and on this the Brits have gone silent, suggesting a climbdown might be on the cards.

"We have not set out a target figure," a British official said. "But you can get tens of billions out from the current figure."

On verra, as they say in Paris which may turn out to be Cameron's biggest problem. The Élysée Palace has signalled it is in no rush to cut a deal and is complaining about the pot of farming subsidies that would be cut by €60bn compared to current budgets under Van Rompuy's scheme. The French also pay a quarter of the UK rebate, and Francois Hollande has been under attack in the French papers this week, with the normally sober Le Monde's front page screaming that Londres is holding the rest of Europe hostage and that Hollande is feckless and lacking a strategy. So he may have to show some sinew.

By Friday lunchtime it should be clear if there is the makings of a deal, in which case a long Brussels weekend beckons. Or they might all just go home after notching up the fifth failure of European leaders in a month.